Fluid flow has two fundamental characteristics. One is that there is no discontinuity of velocity; the second is that, at a solid boundary, the velocity of the fluid relative to the surface is zero. Close to the surface there is therefore a region in which the velocity increases rapidly from zero and approaches the velocity of the main fluid flow stream; this is the boundary layer. The increase in velocity with increasing distance from the solid boundary involves relative movement between the particles in the boundary layer and shear stresses here are therefore of prime importance. The fluid flow in the boundary layer immediately adjacent to the solid boundary is laminar.
The shear force on the solid boundary of an object, both in magnitude and direction, is one of the most important parameters when determining the hydrodynamic or aerodynamic performance of the object and in studying the flows around the object, especially flows near the walls of the object. The magnitude and the direction of the shear force can be used to calculate the overall drag as well as to predict the separation lines of flows on the surface of the object.
There are a number of techniques available for the measurement of shear forces in fluid flow, such as the Preston tube, hob film techniques and the direct measurement technique.
The Preston tube, a type of pressure sensing tube, is used to measure the pressure of the fluid. The pressure can be regarded as a function of the non-dimensional velocity profile, which is non-dimensioned by the inclusion of a term for the shear stress at the boundary. Therefore, the measurement of pressure is directly linked to the measurement of shear stress. Once the pressure is measured, the shear stress can be obtained indirectly according to the relationship between the two variables. This method, however, depends on the knowledge of the velocity profile which can only be known with any precision in a very limited number of cases.
Turning to hot-wire and hot-film techniques, when a high temperature object is placed in a lower temperature environment the heat will transfer from the hot object to the cold environment, the heat transfer being a nonlinear function of the temperatures of both the hot object and the cold environment, as well as the velocity profile of the fluid flow around the hot object, and a number of other thermodynamic parameters. The hot-film technique employs a thin platinum film fused to a support which is heated, and the heat loss from the hot film is measured in order to calculate the shear stress according to the relationship between the heat transfer and the velocity profile of the flows, according to a calibrated temperature-velocity profile. However, the heat transfer from the hot film often causes a change in temperature of the adjacent solid surface and the surrounding fluid, thus disturbing the flow field. As a result, the measurement and the calibration may not be accurate. Moreover, the output is nonlinear, whilst the signal-to-noise ratio is small and the frequency response poor compared to ordinary hot-wire techniques. Thus, the use of the hot-film technique is cumbersome and somewhat unreliable, and such techniques are limited in application.
Direct measurement sensors are also known. A typical such sensor is the so-called xe2x80x9cfloating elementxe2x80x9d sensor, and one such floating element sensor is disclosed in U.S. Pat. No. 4,896,098 by Haritonidis et al, issued on Jan. 23, 1990. The sensor disclosed comprises a micro-dimensioned square plate suspended above a substrate by four micro-dimensioned support arms. The micro size of the sensor substantially reduces the pressure gradient across the plate, and the sensor enables the resolving of very small fluctuations in turbulent flow fields. Furthermore, the plate is suspended at a height above the substrate which forms a very small passageway or cavity between the plate and substrate. The dimensions of the passageway are so small that vertical (ie. normal to the surface of the plate) movement of the plate by forces due to vibration is heavily suppressed by viscous damping within the passageway. The dimensions of the plate and the damping effect of the passageway enable the micro-dimensioned sensor to be substantially insensitive to vertical forces yet sensitive to shear forces acting one it. Readout means which are also substantially insensitive to vertical movement are incorporated in the sensor to provide an indication of sensed shear stress. However, the patent does not consider the measurement of the direction of the shear forces in a single measuring element, nor is the sensor able to be used to measure this direction. The direction of the shear force acting at a solid boundary is essential to describe the patterns of sheer stress and to determine the separation lines or points in laminar or turbulent fluid flows. Moreover, the sensor described in this patent is somewhat limited in its sensitivity.
Moreover, the sensor described in this prior art document is somewhat limited in its sensitivity.
The invention provides a sensor for measuring shear stress at a solid boundary in a fluid flow including a floating element arranged for resilient movement in all directions in a single plane for measuring shear stress in that plane. The element is spaced from a substrate to form a cavity therebetween. The substrate includes a two-dimensional array sensors for measuring the displacement of the element in both magnitude and direction.
The present invention therefore provides a sensor for measuring shear forces at a solid boundary which addresses the shortcomings of the prior art. In particular, the present invention provides a floating element shear force sensor which is suitable for measuring both the magnitude and direction of the shear force in a single sensor unit.
In a preferred form, the two-dimensional array includes a two-dimensional array of conductive plates provided in or on said substrate, said floating element comprising a further conductive plate, and said array of conductive plates being electrically connectable to an output to provide a measure of the displacement of said floating element in said plane.
Preferably, the floating element is suspended for movement in said plane relative to the substrate by a plurality of meandering support arms, having preferably a zig-zag form, and these support arms advantageously may have a significantly higher bending stiffness in a direction normal to said plane than in a direction in said plane. The displacement sensitivity to shear force of the device is preferably at least about 1.4 xcexcm/Pa.
In a preferred form, the array of substrate conductive plates includes a first plate positioned centrally relative to the floating element and four outer plates substantially uniformly distributed around the periphery of and spaced from said first plate, each of said conductive plates being connectable to output circuitry to provide measures representative of the shear stress acting on said floating elements.
In one form of the invention, said floating element is constituted in its entirety by said floating further conductive plate.
The floating element may comprise a square plate, suspended by four meandering support arms in the plane of the floating element, or alternatively may comprise a circular plate, suspended by three meandering support arms.
Ideally, the floating element is sufficiently small that the pressure over the floating element is substantially uniform and the pressure gradient thereacross substantially negligible, and the cavity between the floating element and the substrate being sufficiently thin that the floating element is effectively damped against vibration, the sensor therefore being highly insensitive in a direction normal to said plane.
Preferably, the floating element has a maximum dimension of less than about 1000 microns, preferably less than about 400 microns, and the cavity is less than about 10 microns in thickness, ideally less than 2 microns.
For measuring shear stress at the solid boundary of an object in a fluid flow field, the sensor may be mounted to the object such that the surface of the floating element lies substantially flush with the surface provided by the solid boundary, and to this end the sensor may be suspended within a recess provided in the solid boundary of the object.
In a preferred form, the floating element and the conductive plates are fabricated by photolithographic micromachining techniques, which also enables constituent electrodes and solid state circuit components to be fabricated in like manner.
The sensor may sense capacitive coupling between the conductive capacitor plates as said floating element displaces and includes at least two matched field effect transistors, one transistor coupled to a first sensing node to sense change in capacitive coupling between the conductive plate of the floating element and one of the substrate conductive plates, and the other transistor coupled to a second sensing node to sense change in capacitive coupling between the conductive plate of the floating element and another one of the substrate conductive plates.
In a preferred form, the sensor includes two pairs of matched field effect transistors, each pair sensing change in capacitive coupling between the conductive plate of the floating element and two of said four outer substrate conductive plates, said first central substrate conductive plate being arranged to receive a constant AC drive signal.
In a further aspect, the invention provides a method for measuring shear stress at a solid boundary in a fluid flow including the steps of:
providing at said solid boundary a floating element arranged for resilient movement in all directions in a single plane, said element being spaced from a substrate to form a cavity therebetween,
providing said substrate with a two-dimensional array providing signals representing a measure of the displacement of said floating element in said plane; and
processing said signals to provide an output representing the magnitude and direction of the shear stress at said solid boundary.
In a preferred form, said floating element comprises a conductive plate and said substrate is provided with a two-dimensional array of conductive plates. The conductive plates of said substrate array are electrically connected to provide said signals representative of the capacitive coupling between the floating element conductive plate and the individual conductive plates of said substrate array.